A large number of computer vision algorithms for finding intensity edges, as well as for performing other vision functions, have been developed within the framework of minimizing an associated "energy" functional. Such a variational formalism is attractive because it allows a priori constraints to be explicitly stated. The single most important constraint is that the physical processes underlying image formation, change slowly in space. For example, the depths of neighboring points on a surface are usually very similar. Standard regularization algorithms embody this smoothness constraint and lead to quadratic variational functionals with a unique global minimum. These quadratic functionals can be mapped onto linear resistive networks, such that the stationary voltage distribution, corresponding to the state of least power dissipation, is equivalent to the solution of the variational functional. Smoothness breaks down, however, at discontinuities caused by occlusions or differences in the physical processes underlying image formation (e.g., different surface reflectance properties). Detecting these continuities becomes crucial, not only because otherwise smoothness is incorrectly applied, but also because the locations of discontinuities are usually required for further image analysis and understanding.
The zero-crossings of the Laplacian of the Gaussian, .gradient..sup.2 G are often used for detecting edges. It is straightforward to show that these zero-crossings usually correspond to the location of edges. Laplacian filters, which have been used widely in computer vision systems, can be approximated by the difference of two Gaussians with different space constants. These filters have been used to help computers localize objects. They work because discontinuities in intensity frequently correspond to object edges.
The present invention takes the difference of two resistive-network smoothings of one-dimensional photoreceptor input signals and finds the resulting zero-crossings. The Green's function of the resistive network, a decaying exponential, differs from the Gaussian, but simulations with digitized camera images have shown that the difference of exponentials gives results nearly as good as the difference of Gaussians. Furthermore, resistive networks have a natural implementation in silicon, while implementing the Gaussian is cumbersome. Resistive networks are described in a book entitled Analog VLSI and Neural Systems by Carver Mead, published in 1989 by Addison Wesley Publishing Company and specifically in Appendix C of that book, beginning at page 339. In addition, the application of a single resistive network to edge-enhancement for different values of the space constant of such resistive network is discussed in the aforementioned Carver Mead book beginning at page 272. However, neither the aforementioned Carver Mead reference, nor any other prior art reference known to the applicants herein, has disclosed the use of the difference in voltages between two resistive networks to detect edges, nor is there any known disclosure of a complete circuit for indicating the detection of edges in a computer vision system and for providing a threshold which is adjustable for permitting the recognition of only significant changes in light intensity, whereby to overcome noise-induced small changes in light intensity which are not likely to be indicative of a true edge.